Mechanics of Continuum Robots with External Loading and General Tendon Routing

Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 79)

Abstract

Routing tendons in straight paths along an elastic backbone is a widely used method of actuation for continuum robots. Tendon routing paths which are general curves in space enable a much larger family of robots to be designed, with configuration spaces and workspaces that are unattainable with straight tendon routing. Harnessing general tendon routing to extend the capabilities of continuum robots requires a model for the kinematics and statics of the robot, which is the primary focus of this paper. Our approach is to couple the classical Cosserat theories of strings and rods using a geometrically exact derivation of the distributed loads that the tendons impose along the robot. Experiments demonstrate that the model accurately predicts tip position to 1.7% of the total arc length, on a prototype robot that includes both straight and helical tendon routing and is subject to both point and distributed loads.

Keywords

Error Straight Prototype Robot Tendon Load Continuum Robot Tendon Tension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Robinson, G., Davies, J.B.C.: Continuum robots – a state of the art. In: IEEE International Conference on Robotics and Automation, pp. 2849–2854 (1999)Google Scholar
  2. 2.
    Trivedi, D., Rahn, C.D., Kierb, W.M., Walker, I.D.: Soft robotics: Biological inspiration, state of the art, and future research. Applied Bionics and Biomech. 5, 99–117 (2008)CrossRefGoogle Scholar
  3. 3.
    Webster III, R.J., Jones, B.A.: Design and kinematic modeling of constant curvature continuum robots: A review. Int. J. of Robotics Research 29, 1661–1683 (2010)CrossRefGoogle Scholar
  4. 4.
    Trivedi, D., Lotfi, A., Rahn, C.: Geometrically exact models for soft robotic manipulators. IEEE Transactions on Robotics 24, 773–780 (2008)CrossRefGoogle Scholar
  5. 5.
    Wilson, J., Mahajan, U.: The mechanics of positioning highly flexible manipulator limbs. J. Mechanisms, Transmissions, Autom. Des. 111, 232–237 (1989)CrossRefGoogle Scholar
  6. 6.
    Xu, K., Simaan, N.: Analytic formulation for kinematics, statics and shape restoration of multi-backbone continuum robots via elliptic integrals. ASME Journal of Mechanisms and Robotics 2, 011 006-1–011 006-13 (2010)Google Scholar
  7. 7.
    Rucker, D.C., Jones, B.A., Webster III, R.J.: A geometrically exact model for externally loaded concentric-tube continuum robots. IEEE Trans. on Robotics 26, 769–780 (2010)CrossRefGoogle Scholar
  8. 8.
    Lock, J., Laing, G., Mahvash, M., Dupont, P.E.: Quasistatic modeling of concentric tube robots with external loads. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2325–2332 (2010)Google Scholar
  9. 9.
    Camarillo, D.B., Milne, C.F., Carlson, C.R., Zinn, M.R., Salisbury, J.K.: Mechanics modeling of tendon-driven continuum manipulators. IEEE Transactions on Robotics 24(6), 1262–1273 (2008)CrossRefGoogle Scholar
  10. 10.
    Gravagne, I.A., Rahn, C.D., Walker, I.D.: Large-deflection dynamics and control for planar continuum robots. IEEE/ASME Trans. on Mechatronics 8, 299–307 (2003)CrossRefGoogle Scholar
  11. 11.
    Buckingham, R., Graham, A.: Reaching the unreachable - snake arm robots. In: International Symposium of Robotics, OCRobotics Ltd. (2003), http://www.ocrobotics.com
  12. 12.
    Chirikjian, G.S.: Hyper-redundant manipulator dynamics: A continuum approximation. Advanced Robotics 9(3), 217–243 (1995)CrossRefGoogle Scholar
  13. 13.
    Chirikjian, G.S., Burdick, J.W.: Kinematically optimal hyper-redundant manipulator configurations. IEEE Transactions on Robotics and Automation 11, 794–806 (1995)CrossRefGoogle Scholar
  14. 14.
    Li, C., Rahn, C.D.: Design of continuous backbone, cable-driven robots. ASME Journal of Mechanical Design 124(2), 265–271 (2002)CrossRefGoogle Scholar
  15. 15.
    Davis, J.H., Hirschorn, R.M.: A model for the embedded tendon control of a slender three-dimensional flexible robot link. Dynamics and Control 4, 185–208 (1994)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Gravagne, I.A., Walker, I.D.: Manipulability, force, and compliance analysis for planar continuum robots. IEEE Trans. on Robotics and Automation 18, 263–273 (2002)CrossRefGoogle Scholar
  17. 17.
    Jones, B., Gray, R., Turlapati, K.: Three dimensional statics for continuum robotics. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2659–2664 (2009)Google Scholar
  18. 18.
    Murray, R.M., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)MATHGoogle Scholar
  19. 19.
    Antman, S.S.: Nonlinear Problems of Elasticity, 2nd edn. In: Antman, S., Marsden, J., Sirovich, L. (eds.) Springer Science (2005)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringVanderbilt UniversityNashvilleUSA

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